It has been one of the benchmark examples in discovering models using data, see, e.g., [1]}, [2]} but there, it is assumed that the dynamics can be given sparsely in a high-dimensional feature dictionary. Here, we do not make any such assumptions and instead learn the vector field using a neural network along the line of [3]}. For this example, we take \(2~500\)  data points in the time interval \([0,10]\)  by simulating the model using the initial condition \([2,0]\)  as done in [3]}. We add various levels of noise in the clean data to have noisy measurements synthetically. We, again, perform similar experiments as done in the previous example. We construct neural networks for implicit representation and the vector field with the parameters given in tab:NNinfoODE.
